Dynamic Leveraging–Deleveraging Games

Abstract

We endogenize the dynamics of a large borrower’s leverage based on a new type of game among the lender, the leveraging/deleveraging game. Leverage is mean reverting around a long-run level and explosive above an instability level. This is driven by the changing nature of the lenders’ game from strategic substitutability to one-sided strategic complementarity: When leverage is below the instability level, the firm is not in danger of default, and the strategic substitutability in the payoff structure acts as a counterbalance on leverage, which is pushed down to the long-run level. If the leverage reaches above the instability level, then it becomes explosive: The strategic complementarity leads to spiraling effects that end in default. We validate our model empirically using aggregate returns of financial firms over the last two decades.